2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172413We develop an alternative scaling approach to determine the criteria for Anderson localization in one-dimensional tight-binding models with random site energies having a bandwidth that decays as a power law in space, $H_{ij} \propto |i - j|^{-α}$. At the first order in perturbation theory the scale dependence of the exchange-narrowed energy of the disorder is compared to the energy level spacing of the ideal system to establish whether or not the disorder has a perturbative effect on the Bloch states. We find that at $α=1$, the perturbative condition is satisfied and for sufficiently weak disorder strength all states are extended. For $α> 1$, all states are localized for arbitrary disorder strength, in agreement with the earlier renormalization group treatment by Levitov.4 Pages, 1 eps figureDisordered Systems and Neural Networkstext